A Simple "Boxed Molecular Kinetics" Approach To Accelerate Rare Events in the Stochastic Kinetic Master Equation.

Robin Shannon,David R Glowacki

doi:10.1021/acs.jpca.7b12521

Abstract

The chemical master equation is a powerful theoretical tool for analyzing the kinetics of complex multiwell potential energy surfaces in a wide range of different domains of chemical kinetics spanning combustion, atmospheric chemistry, gas-surface chemistry, solution phase chemistry, and biochemistry. There are two well-established methodologies for solving the chemical master equation: a stochastic "kinetic Monte Carlo" approach and a matrix-based approach. In principle, the results yielded by both approaches are identical; the decision of which approach is better suited to a particular study depends on the details of the specific system under investigation. In this Article, we present a rigorous method for accelerating stochastic approaches by several orders of magnitude, along with a method for unbiasing the accelerated results to recover the "true" value. The approach we take in this paper is inspired by the so-called "boxed molecular dynamics" (BXD) method, which has previously only been applied to accelerate rare events in molecular dynamics simulations. Here we extend BXD to design a simple algorithmic strategy for accelerating rare events in stochastic kinetic simulations. Tests on a number of systems show that the results obtained using the BXD rare event strategy are in good agreement with unbiased results. To carry out these tests, we have implemented a kinetic Monte Carlo approach in MESMER, which is a cross-platform, open-source, and freely available master equation solver.

Highlights

Predicting the rate of chemical transformations is of fundamental importance to an array of scientific endeavors from atmospheric[1] and combustion chemistry modeling[2] to protein folding[3] and drug binding.[4]
To test the stochastic master equation solver implemented in MESMER, we examined a model system based upon the acetyl + O2 reaction system, which is part of the MESMER test suite and has been studied extensively by several groups using both matrix and kinetic Monte Carlo (KMC) energy grained master equation (EGME)’s
In this study we have outlined the boxed molecular kinetics” (BXK) acceleration methodology, which has been implemented within the MESMER software package, and has the potential to accelerate rare event sampling in a stochastic trajectory by several orders of magnitude

Summary

INTRODUCTION

Predicting the rate of chemical transformations is of fundamental importance to an array of scientific endeavors from atmospheric[1] and combustion chemistry modeling[2] to protein folding[3] and drug binding.[4]. The KMC approach to solving the EGME involves running a range of Monte Carlo “trajectories”, each of which has a prespecified time step, until statistical convergence is achieved In this respect, the KMC approach has similarities with molecular dynamics simulations. In order to demonstrate the acceleration afforded by the BXK algorithm, we have implemented a KMC algorithm in the EGME code MESMER.[19] This is only the second example[31] of a code in which both matrix approaches and KMC methods are available in the same framework As such, it offers an ideal opportunity for the chemical kinetics community to better evaluate the relative merits of each approach in a wide range of chemically important systems.

MASTER EQUATION METHODOLOGY AND IMPLEMENTATION IN MESMER

THE BXK RARE EVENT ACCELERATION ALGORITHMS

CONCLUSIONS

■ REFERENCES